a cylindrical container of three rubber balls has a height of 18 centimeters and a diameter of 6 centimeters. each ball in the container has a radius of 3 centimeters. find the amount of space in the container that is not occupied not not rubber balls. round your answer to the nearest whole number
the amount of empty space in the container is about □ cubic centimeters

Question

Accepted Answer

# Explanation:
## Step1: Calculate the volume of the cylinder
The formula for the volume of a cylinder is $V_{cylinder}=\pi r^{2}h$. Given that the diameter $d = 6$ cm, so the radius $r=\frac{d}{2}=3$ cm and the height $h = 18$ cm.
$$
\begin{align*}
V_{cylinder}&=\pi\times(3)^{2}\times18\
&=\pi\times9\times18\
&=162\pi
\end{align*}
$$
## Step2: Calculate the volume of one rubber - ball
The formula for the volume of a sphere is $V_{sphere}=\frac{4}{3}\pi r^{3}$. Given $r = 3$ cm.
$$
\begin{align*}
V_{sphere}&=\frac{4}{3}\pi\times(3)^{3}\
&=\frac{4}{3}\pi\times27\
&=36\pi
\end{align*}
$$
## Step3: Calculate the volume of three rubber - balls
Since there are three rubber - balls, $V_{three - spheres}=3\times V_{sphere}$
$$
\begin{align*}
V_{three - spheres}&=3\times36\pi\
& = 108\pi
\end{align*}
$$
## Step4: Calculate the unoccupied volume
The unoccupied volume $V=V_{cylinder}-V_{three - spheres}$
$$
\begin{align*}
V&=162\pi-108\pi\
&=54\pi\
&\approx54\times3.14\
& = 169.56
\end{align*}
$$

# Answer:
$170$

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the volume of the cylinder

Step2: Calculate the volume of one rubber - ball

Step3: Calculate the volume of three rubber - balls

Step4: Calculate the unoccupied volume

Answer: